Melt growth is the most important growth method for the production of bulk single crystals of semiconductors, oxides, metals and other materials. Its technology can only be understood or improved by a profound knowledge of the underlying fundamentals, like phase diagrams,
growth kinetics, heat and species transport. This article treats relevant aspects of these fundamentals in close correlation to the most important melt growth processes, the Czochralski and Gradient Freeze (Bridgman) methods.

This tutorial lecture explains the ways supersaturation in complex solutions may be introduced to be most relevant to describe experimental data on kink and step kinetics. To do so, we express the kink rate via the frequencies of attachment and detachment of the building units and then link these frequencies to the measurable activities of these units in solution. Possible reasons for violation of the Gibbs‐Thomson law are also briefly discussed with reference to our earlier work.

The first success with the growth of semiconductor materials by vapor phase epitaxy (VPE) dates back to the 1950’s. Today, it is the largest volume technique for the production of both Si and III/V electronic and photonic devices. Of course, commercial processes for the growth of Si layers, dielectrics, and metals are part of a multi‐billion dollar industry. Even for the III/V semiconductors commercial reactors can be purchased yielding 2000 cm2/run, mainly for the production of light emitting diodes and solar cells. The various vapor phase epitaxial processes share a basic underpinning of thermodynamics and kinetics. The vehicle used for this paper will be mainly the organometallic growth of III/V materials. It will briefly discuss key concepts in our understanding of the complex growth process, including both kinetic and thermodynamic aspects of vapor growth. Special attention will be paid to surface processes and the use of surfactants to control the properties of the resulting materials. Our understanding of this topic is still developing rapidly.

This chapter gives a general overview of the defect types and their origins at the bulk crystal
growth. The role of thermodynamics, kinetics, convection, segregation, thermomechanical stress and non‐stoichiometry are considered. The possible influence of the structure of the fluid phase is implied. Results of modelling and practical measures of in situ defect control are presented. Strong emphasis is given to semiconductor crystal growth from melt. The defects are treated in the classical manner: 0‐, 1‐, 2‐ and 3‐dimensional ones, i.e. point defects, impurity and dopant distributions, dislocations,
cell
structures and second phase particles. After the generation and incorporation mechanisms of point defects are discussed micro‐ and macrosegregation phenomena, i.e. striation formation and the effect of constitutional supercooling are added. Then the formation and multiplication of dislocations and their collective interactions, leading to cell
structuring, are shown. The importance of temperature field engineering is underlined. Selected two‐dimensional defects like facets and twins are delineated next. Finally, second phase precipitation and inclusion trapping are discussed. The importance of in situ stoichiometry control is accentuated.

We present an overview of in‐situ experiments to study molecular beam epitaxial growth by x‐ray diffraction and high‐energy electron diffraction. The applicability of kinematic
theory allows a quantitative evaluation of the surface kinetics on compound semiconductor surfaces; GaAs(001), InAs(001) and GaSb(001) are presented as examples. Both the growth in the layer‐by‐layer mode and the recovery can be analyzed in considerable detail. As an example of heteroepitaxy, the nucleation and relaxation of hexagonal MnAs on GaAs(001) is presented. We find an extremely anisotropic interface structure with a periodic array of misfit dislocations that can be quantitatively analyzed.

In this lecture I present an introduction to the time‐resolved observation of atomic transport processes on metal surfaces using scanning tunneling microscopy video sequences. The experimental data is analyzed using scaling law concepts known from statistical thermodynamics. I will present studies from metal surfaces in vacuum as well as in electrolyte.

We present an overview of mathematical models and their large‐scale numerical solution for simulating different phenomena and scales in melt and solution
crystal growth. Samples of both classical analyses and state‐of‐the‐art computations are presented. It is argued that the fundamental multi‐scale nature of crystal growth precludes any one approach for modeling, rather successful crystal growth modeling relies on an artful blend of rigor and practicality.

This course is aimed at showing how to understand and solve problems of melt flow under magnetic fields during crystal growth from the melt. The course involves the following points. The first part of the course focuses on an analytical approach for determining the effects of external forces based on gravitational acceleration and of rotations of a crystal and a crucible on convection. Analysis of the effects of electric, magnetic and electromagnetic forces on the melt convection will be also introduced.

Crystal growth morphology results from an interplay of crystallographic anisotropy and growth kinetics, the latter consisting of interfacial processes as well as long‐range transport. Mathematical modeling of crystal growth shapes is important to our understanding of fundamental crystal growth phenomena as well as to improvement and optimization of practical processes for crystal growth. Such modeling results in a difficult free boundary problem because one must piece together solutions of partial differential equations, via boundary conditions, on a crystal surface whose location and shape are yet to be determined. Moreover, this problem is complicated because the nature of long‐range transport leads to natural instabilities of shape, so‐called morphological instabilities, on the scale of the geometric mean of a transport length and a capillary length. The resulting shapes can be cellular or dendritic but can also exhibit corners and facets related to the underlying crystallographic anisotropy.
Growth subsequent to morphological instability can be modeled by means of the phase field model, which is a mesoscopic diffuse interface model that eliminates interface tracking. The phase field is an auxiliary parameter that identifies the phase; it is continuous but makes a transition over a thin region, the diffuse interface, from its constant value in a crystal to some other value in the nutrient phase. Coupled partial differential equations that govern the time evolution of the phase field and accompanying fields (such as temperature and composition) can be formulated on the basis of an entropy functional and irreversible thermodynamics. Anisotropies can also be incorporated. Examples of computed cellular and dendritic morphologies show the transition from shallow to deep cells, liquid encapsulation, dendritic sidebranching, tip splitting, coarsening, solute microsegregation and many other phenomena that have been observed experimentally. This presentation will emphasize the fundamentals of phase field theory and also introduce more recent developments such as crystal phase field theory, which is based on density functional theory and incorporates some aspects of crystallinity, as well as Lattice Boltzmann algorithms that may be used to incorporate convection in fluid phases.

We consider homoepitaxy (or low‐misfit heteroepitaxy) via vapor deposition or MBE under UHV conditions. Thin film growth is initiated by nucleation and growth of 2D islands in the submonolayer regime. For atoms subsequently deposited on top of islands, a step edge barrier often inhibits downward transport and produces kinetic roughening during multilayer
growth. Such unstable growth is characterized by the formation of 3D mounds (multilayer stacks of 2D islands). Kinetic Monte Carlo
(KMC) simulation of suitable atomistic lattice‐gas models can address fundamental or general issues related to both submonolayer and multilayer film evolution, and can also provide a predictive tool for morphological evolution in specific systems. Examples of the successes of KMC modeling are provided for metal homoepitaxial film growth, specifically for contrasting behavior in the classic Ag/Ag(100) and Ag/Ag(111) systems.

With the introduction of nanoscale in situ imaging technologies, a new understanding of the microscopic processes that underlie widely used empirical ‘rate laws’ is emerging. This review summarizes recent findings that the kinetics of mineral dissolution can be explained by equivalent, but inverse, microscopic processes that have been used to describe growth. Like growth, dissolution occurs by multiple microscopic processes — each with an empirical and mechanism‐based rate law and a unique dependency upon chemical driving force. As undersaturation departs from equilibrium, dissolution rates are first dominated by the process of step propagation, followed by generation of steps at dislocation sources, and then by nucleation of vacancy islands. Interplays between step edge energy, temperature and other parameters determine if/when minerals express all of these processes across driving force. Net rates that are measured from reactor studies to give power law dependencies upon driving force describe the sum of these processes. Central to understanding these relations is the pivotal roles of process‐specific energy barriers to reactions at different surface structures and defects of minerals and materials.

Crystallization from solution underlies numerous laboratory, industrial, and biological processes. Because of the high surface free energy between the crystal and the solution, the interface between crystal and its growth medium is smooth and comprised of singular crystal faces. On such smooth interfaces, the locations at which a molecule from the solution can associate to the crystal, the kinks, are few and located along the edges of unfinished crystalline layers, the steps. The rate of step propagation, and through it, the rate of growth of a crystal from solution, is determined by the kink density and by the kinetics of incorporation into the kinks. In turn, the latter depends on the free energy barriers for incorporation. Here, three mechanisms of generation of kinks are discussed: by thermal fluctuations of the steps, suggested by J.W. Gibbs, by one‐dimensional nucleation of new crystalline rows, and by association to the steps of two‐dimensional clusters, preformed on the terraces between the steps. The latter two mechanisms only operate in the cases where the kink density, determined by the thermal fluctuations, is low. The rate of incorporation into kinks follows Kramers‐type kinetics, in which the transition over the free energy barrier is governed by diffusion in the solution, in contrast to the Eyring‐type transition state, which decays due to the vibrations of the activated complex. Finally, the barrier is not due to stretched bonds between the incoming molecules and the kink, but rather corresponds to the destruction of the shell of structured water around both the kink and the incoming molecule. The latter two insights allow rationalization of the effects of additives on crystallization kinetics, especially those employed in biological regulation in living organisms.

Molecular simulation techniques represent a powerful complement to experiment for studying the surfaces and interfaces of minerals, not least because we can easily visualize the surface processes. The aim of this presentation is to describe recent work using molecular simulation methods to model the structure, stability and reactivity of mineral surfaces and how the simulation of these properties can be used to predict morphologies. Initially, we will describe how molecular simulation techniques can be used to give a reliable description of the surfaces. One of the significant contributions that atom‐based simulation methods can make is in the investigation of competitive adsorption of impurities at surfaces and several examples are shown. Finally, two approaches for increasing the scope and reliability of the simulations are discussed, namely, electronic structure calculations, which enable us to explore the mineral surface stoichiometry and potential‐based molecular dynamics simulations, which introduce dynamical contribution to the surface processes and hence allows for detailed characterization of the mineral‐water interface.

Surfactants have been used to alter the growth behavior and structure of epitaxial
films.
Surfactants are characterized by a low vapor pressure, low or negligible solubility in the host material and the ability to segregate to the growing
surface. The change in surface composition due to this surface segregation can lead to a wide range of phenomena resulting in changes to the chemical and physical structure of the growing
film. Thermodynamic and kinetic considerations associated with the influence of surfactant during the growth of lattice mismatched semiconductors are presented.

X‐ray diffraction allows the determination of the structure and morphology of crystals growing in a wide range of environments. After an introduction of the technique, recent results are shown on the structure at solid‐liquid interfaces. It is found that both sides of the interface differ from their bulk structure: at the crystalline part relaxation and/or chemisorption may occur, while the interfacial liquid can show significant ordering. These effects will modify the growth behavior, but current growth theories do not yet incorporate such details. The evolution of the surface roughness and morphology during growth is a second application of X‐ray diffraction that is being applied for an ever increasing range of deposition techniques.

Although conventional optical interferometry has lower resolution for the observation of crystal surfaces than scanning probe microscopy
(SPM) such as AFM or STM, new advanced interferometers have attained nearly the same resolution as scanning microscopes. The advantages of using optical interferometers can be summarized as follows: (1) they can be used not only at room temperature but also at elevated temperatures as high as 1800K; (2) their ability to resolve time is much better, making them more suitable for observing rapidly growing crystals; and (3) they observe surfaces non‐destructively, making in situ observation possible if the solution or the melt is transparent. In this lecture, the key points of observing growth steps and measuring growth rate will be introduced together with recently developed interferometry such as Laser Confocal Phase‐Shift Interferometry (LCPSI). Using this technique, mono‐molecular growth steps of proteins and some other crystals can be observed with accurate step height and growth or dissolution rates as slow as 10−5nm/s (1μm/year) can be measured.

Over the past decade there has been a natural drive to extend the investigation of dynamic surfaces in fluid environments to higher resolution characterization tools. Various aspects of solution crystal growth have been directly visualized for the first time. These include island nucleation and growth using transmission electron microscopy and scanning tunneling microscopy; elemental step motion using scanning probe microscopy; and the time evolution of interfacial atomic structure using various diffraction techniques. In this lecture we will discuss the use of one such in situ method, scanning probe microscopy, as a means of measuring surface dynamics during crystal growth and dissolution. We will cover both practical aspects of imaging such as environmental control, fluid flow, and electrochemical manipulation, as well as the types of physical measurements that can be made. Measurements such as step motion, critical lengths, nucleation density, and step fluctuations, will be put in context of the information they provide about mechanistic processes at surfaces using examples from metal and mineral crystal growth.

We discuss the use of dynamic electron microscopy to visualise, in real time, the epitaxial
growth of Si and Ge nanostructures. In situ observations of the formation of quantum dots and nanowires provide real time kinetic information that can be useful in determining the physical processes that control nanostructure growth. By comparing observations made during growth with observations of the same structures made after cooling and air exposure, we demonstrate the uniqueness of the information that can be acquired from dynamic microscopy during growth.

In‐situ analysis of epitaxial
growth is the essential ingredient in order to understand the growth process, to optimize growth and last but not least to monitor or even control the epitaxial
growth on a microscopic scale. In MBE
(molecular beam epitaxy) in‐situ analysis tools existed right from the beginning because this technique developed from Surface Science technology with all its electron based analysis tools (LEED, RHEED, PES etc). Vapour Phase Epitaxy, in contrast, remained for a long time in an empirical stage (“alchemy”) because only post growth characterisations like photoluminescence, Hall effect and electrical conductivity were available. Within the last two decades, however, optical techniques were developed which provide similar capabilities as in MBE for Vapour Phase growth. I will discuss in this paper the potential of Reflectance Anisotropy Spectroscopy (RAS) and Spectroscopic Ellipsometry (SE) for the growth of thin epitaxial semiconductor layers with zincblende (GaAs etc) and wurtzite structure (GaN etc). Other techniques and materials will be also mentioned.

Scitation: PERSPECTIVES ON INORGANIC, ORGANIC, AND BIOLOGICAL CRYSTAL GROWTH: FROM FUNDAMENTALS TO APPLICATIONS: Basedon the lectures presented at the 13th International Summer School on Crystal Growth